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\section{Conclusion}

Cooperation is considered as an important aspect of economic activities for not only companies but the goverment, and how to realize cooperation among these agents has got enormous attention in recent years.
Note that cost sharing is the core problem in
cooperative game, especially in scheduling problems, where costs are hard to allocate.
Instead of giving the specific cost allocation of the cooperative game, we mainly focus on how to provide a way to satisfy all players in the grand coalition.
Concretely, this paper studies how to set an appropriate price by the third-party in the scheduling game to stabilize the grand coalition.

In our study, we stressed the concept of price to provide the appropriate way to stabilize the grand coalition and enhance cooperation opportunities.

Our main results show that ...

Moreover, our analysis provides managerial guidance on how to adjust the price by central authority to
promote collaboration according to the number of machines.
